LINGUISTIC CONTEXT SPACES - NECESSARY FRAMES FOR CORRECT APPROXIMATE REASONING

Effective inference under uncertainty in Artificial Intelligence depen ds on context. Inferences based on Bayesian conditional probabilities use context effectively. However, newer approaches, such as fuzzy reas oning (and others-e.g., Dempster-Shafer, rough sets, etc.) cannot take context appropriately into account without further development of lin guistic context. We develop the new concept of ''context space'' for f uzzy sets theory. Many-valued fuzzy sets were introduced by Nakanishi [1989]. We use them in this paper to describe context (context space) as an analog of probability space. Such a description of context space allows one to usefully construct fuzzy sets for specific applications , and thus improves the foundation for fuzzy sets theory. In addition, the problem of establishing membership functions (MFs) is considered for context spaces. It is shown that semantic operational procedures [ Hisdal, 1984] and modal logic [Resconi, et al., 1992] are preferable w hen used jointly with a complete and exactly defined context space as introduced in the paper. Finally, the theory of fuzzy sets is compared with probability theory in connection with the problem of MF acquisit ion.